Abstract
In this paper we consider the distribution in the half-plane σ>1/2 of the values of DirichletL-series formed with quadratic characters.
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Chowla, S., Erdös, P.: A theorem on the distribution of values ofL-series. J. Indian Math. Soc.15A, 11–18 (1951)
Elliott, P.D.T.A.: On the distribution of the quadratic class number. Mat. Litovsk.10, 189–197 (1970)
Elliott, P.D.T.A.: On the mean value off(p). Proc. Lond. Math. Soc. (3)21, 28–96 (1970)
Elliott, P.D.T.A.: Some applications of a theorem of Raikov to number theory. J. Number Theory2, 22–55 (1970)
Elliot, P.D.T.A.: On distribution functions (mod 1): Quantitative Fourier inversion. Journ. of No. Theory4, 509–522 (1972)
Esseen, C.G.: Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math.77, 1–125 (1945)
Hooley, C.: On the representation of a number as the sum of two squares and a prime. Acta Arith.97, 189–210 (1957)
Lavrik, A.F.: The moments of the number of classes of primitive quadratic forms of negative discriminant. Dokl. Akad. Nauk. SSSR197, 32–35 (1971)
Lavrik, A.F.: A functional equation for DirichletL-series and the problem of divisors in arithmetic progressions. Izv. Akad. Nauk. SSSR Ser. Mat.30, 433–448 (1966)
Prachar, K.: Primzahlverteilung. Berlin-Göttingen-Heidelberg: Springer 1957
Raikov, D.A.: A theorem from the theory of analytic characteristic functions. Izv. NII. mat. mek. f-ta Tomskovo un-ta.2, 8–11 (1938). See also U. V. Linnik: Decomposition of probability distributions. Chapter 4, §4.1. New York: Dover 1964
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The author was partially supported by N.S.F. Grant No. 1765-38.
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Elliott, P.D.T.A. On the distribution of the values of quadraticL-series in the half-plane σ>1/2. Invent Math 21, 319–338 (1973). https://doi.org/10.1007/BF01418793
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DOI: https://doi.org/10.1007/BF01418793